Further Mathematics GCSE
Further Mathematics GCSE glossary
24 key terms for Further Mathematics GCSE, A to Z, each linked to the topic pages that use it.
B
- Basic Variable
- A variable currently included in the solution, corresponding to a column with a single 1 and all other entries 0.OCR
C
- Coefficient of Restitution ($e$)
- A fractional value between 0 and 1 representing the ratio of the relative speed of separation to the relative speed of approach.OCR
H
- Hessian Matrix
- A square matrix of second-order partial derivatives of a function.OCR
I
- Identity
- An equation that is true for all values of the variables, denoted by the triple equals sign (≡).OCR
- Improper Rational Function
- A fraction of polynomials where the degree of the numerator is greater than or equal to the degree of the denominator.OCR
- Impulse
- The change in momentum of an object, equal to the integral of force with respect to time.OCR
- Irreducible Quadratic
- A quadratic expression that cannot be factorised into linear factors over the real numbers (its discriminant b^2 - 4ac < 0).OCR
L
- Line of Centres
- The straight line passing through the centres of two colliding spheres at the instant of impact.OCR
M
- Mixed Derivative Theorem (Clairaut's Theorem)
- The principle that the mixed second partial derivatives are equal: $f_{xy} = f_{yx}$, provided the second partial derivatives are continuous.OCR
- Momentum
- The product of an object's mass and its velocity.OCR
- Monic Polynomial
- A polynomial where the leading coefficient (the coefficient of the highest power of x) is 1.OCR
N
- Non-Basic Variable
- A variable not currently in the solution, which takes a value of zero.OCR
O
- Optimal Solution
- The best possible solution that satisfies all constraints, found when no negative values remain in the objective row.OCR
P
- Partial Derivative
- The derivative of a function of two or more variables with respect to one variable, while the other variables are treated as constants.OCR
- Perfectly Elastic Collision
- A collision where $e=1$.OCR
- Perfectly Inelastic Collision
- A collision where $e=0$.OCR
- Pivot Element
- The element at the intersection of the pivot column and pivot row.OCR
- Proper Rational Function
- A fraction of polynomials where the degree of the numerator is strictly less than the degree of the denominator.OCR
S
- Saddle Point
- A stationary point that is a local maximum in one direction and a local minimum in another direction.OCR
- Simplex Tableau
- A matrix representation of a linear programming problem in standard form.OCR
- Slack Variable
- A variable added to an inequality constraint to transform it into an equation.OCR
- Stationary Point
- A point on a surface where the tangent plane is horizontal; the partial derivatives with respect to all variables are zero.OCR
- Symmetric Function
- An expression involving roots that remains unchanged if any two roots are swapped (e.g., alpha^2 + beta^2).OCR
T
- Tangent Plane
- A plane that touches a surface at a single point and represents the best linear approximation to the surface near that point.OCR
Where these terms come from
Each definition is one we publish on a Further Mathematics GCSE topic page or study guide. Open a term to see how each exam board words it and which topic it belongs to. For the full course, go to Further Mathematics revision or the glossary for every subject.
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